Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated:
1
00:00:03,030 --> 00:00:04,380
Instructor: Welcome back, folks.
2
00:00:04,380 --> 00:00:05,970
This is going to be a short lecture
3
00:00:05,970 --> 00:00:08,823
where we introduce you to the chi-squared distribution.
4
00:00:09,780 --> 00:00:13,200
For starters, we denote a chi-squared distribution
5
00:00:13,200 --> 00:00:16,560
as the capital Greek letter chi squared
6
00:00:16,560 --> 00:00:21,000
followed by a parameter k depicting the degrees of freedom.
7
00:00:21,000 --> 00:00:22,320
Therefore, we read the following
8
00:00:22,320 --> 00:00:26,850
as variable Y follows a chi-squared distribution
9
00:00:26,850 --> 00:00:28,350
with three degrees of freedom.
10
00:00:30,000 --> 00:00:31,833
All right, let's get started.
11
00:00:33,240 --> 00:00:37,290
Very few events in real life follow such a distribution.
12
00:00:37,290 --> 00:00:39,510
In fact, chi-squared is most featured
13
00:00:39,510 --> 00:00:42,810
in statistical analysis when doing hypothesis testing
14
00:00:42,810 --> 00:00:44,793
and computing confidence intervals.
15
00:00:45,900 --> 00:00:48,270
In particular, we most commonly find it
16
00:00:48,270 --> 00:00:51,663
when determining the goodness of fit of categorical values.
17
00:00:52,620 --> 00:00:54,660
That is why any example we could give you
18
00:00:54,660 --> 00:00:56,370
would feel extremely convoluted
19
00:00:56,370 --> 00:00:58,893
to anyone not familiar with statistics.
20
00:01:01,140 --> 00:01:03,690
All right, now let's explore the graph
21
00:01:03,690 --> 00:01:05,403
of the chi-squared distribution.
22
00:01:06,990 --> 00:01:09,450
Just by looking at it, you can tell the distribution
23
00:01:09,450 --> 00:01:13,320
is not symmetric, but rather asymmetric.
24
00:01:13,320 --> 00:01:16,080
Its graph is highly skewed to the right.
25
00:01:16,080 --> 00:01:19,290
Furthermore, the values depicted on the x-axis
26
00:01:19,290 --> 00:01:22,023
start from zero rather than a negative number.
27
00:01:23,190 --> 00:01:27,300
This, by the way, shows you yet another transformation.
28
00:01:27,300 --> 00:01:30,630
Elevating the student's T distribution to the second power
29
00:01:30,630 --> 00:01:33,543
gives us the chi-squared, and vice versa.
30
00:01:34,380 --> 00:01:37,620
Finding the square root of the chi-squared distribution
31
00:01:37,620 --> 00:01:39,423
gives us the students t.
32
00:01:41,850 --> 00:01:43,890
Great, so a convenient feature
33
00:01:43,890 --> 00:01:45,660
of the chi-squared distribution
34
00:01:45,660 --> 00:01:48,630
is that it also contains a table of known values,
35
00:01:48,630 --> 00:01:51,723
just like the normal or students T distributions.
36
00:01:53,010 --> 00:01:55,950
The expected value for any chi-squared distribution
37
00:01:55,950 --> 00:01:59,463
is equal to its associated degrees of freedom, k.
38
00:02:00,510 --> 00:02:04,260
Its variance is equal to two times the degrees of freedom,
39
00:02:04,260 --> 00:02:06,273
or simply two times k.
40
00:02:07,950 --> 00:02:09,810
To learn more about hypothesis testing
41
00:02:09,810 --> 00:02:11,130
and confidence intervals,
42
00:02:11,130 --> 00:02:14,567
you can continue with our program where we dive into those.
43
00:02:15,480 --> 00:02:17,490
For now, you know all you need to
44
00:02:17,490 --> 00:02:19,293
about the chi-squared distribution.
45
00:02:20,550 --> 00:02:21,603
Thanks for watching.
3621
Can't find what you're looking for?
Get subtitles in any language from opensubtitles.com, and translate them here.